Question #43672

Two distant, mutually incoherent point sources $S_1$ and $S_2$ emit linearly polarized light of wavelength $\lambda = 500\text{ nm}$. The electric field vector of the emitted light from both sources makes an angle of $45^\circ$ with the vertical. A telescope is used to observe these sources. The telescope has a rectangular aperture of width $a = 2.0 \times 10^{-3}\text{ m}$ (horizontal) and height $b = 5.0 \times 10^{-3}\text{ m}$ (vertical). A special mask is placed over the aperture: the left half ($-a/2 \le x \le 0$) is covered by an ideal linear polarizer with its transmission axis vertical, and the right half ($0 \le x \le a/2$) is covered by an ideal linear polarizer with its transmission axis horizontal. What is the minimum angular separation $\theta_{min}$ between the two sources along the horizontal direction such that they are just resolved according to the Rayleigh criterion?